Abstract Estimates are obtained for the safe spacing between a given number of similar fissile spheres arranged in a linear, square, or cubic array. These estimates give upper bounds, so that they overestimate the size of the least spacing that is safe. Estimates are also obtained for the number of fissile spheres that may be stored safely in a regular linear, square, or cubic array, with given spacing between spheres. These estimates give lower bounds, so that they underestimate the maximum number that can be stored safely. The assumptions used in these calculations are stated, the chief one being that the probability of direct neutron passage from one sphere to another decreases at least as fast as the reciprocal of the distance between them. Some numerical examples are calculated. General arrays of fissile bodies are also considered briefly.